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Homework Help: Real and apparent depth

  1. Sep 29, 2010 #1
    Hi all, I have this problem :

    A coin is dipped to the bottom of a water filled container made of an opaque material. Observed from the water surface, the depth of the coin appears to be 2 meters. Find the real depth ( R.I. of water = 1.33 )

    Since angles are not given, how do I apply snell's law here ? I would normally find the tangent values of angles of incidence and refraction but as angles are not given, I cannot derive the real depth that way. Sines are not helping here. See attached diagram for reference ( MSPaint work, so might be bad ) - snell's law allows me to find the ratio of CD and BD. After that, I can't do anything.

    [PLAIN]http://img638.imageshack.us/img638/4082/38043092.png [Broken]
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 29, 2010 #2

    Doc Al

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    Staff: Mentor

    Hint: Consider that you are observing the coin from almost directly above. So the angles of incidence and refraction are small.
     
  4. Sep 29, 2010 #3
    How'd that help, exactly ? What difference does that make ?
     
  5. Sep 29, 2010 #4

    Doc Al

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    sinθ ≈ tanθ, for one.
     
  6. Sep 29, 2010 #5
    Surely such approximations would lead to slight inaccuracies. What angular ranges are we talking about ?
     
  7. Sep 29, 2010 #6

    Doc Al

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    Staff: Mentor

    Play around with some angles and see.
     
  8. Sep 29, 2010 #7
    I would if you suggested me a range .
     
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